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2020 A phase transition for preferential attachment models with additive fitness
Bas Lodewijks, Marcel Ortgiese
Electron. J. Probab. 25: 1-54 (2020). DOI: 10.1214/20-EJP550


Preferential attachment models form a popular class of growing networks, where incoming vertices are preferably connected to vertices with high degree. We consider a variant of this process, where vertices are equipped with a random initial fitness representing initial inhomogeneities among vertices and the fitness influences the attractiveness of a vertex in an additive way. We consider a heavy-tailed fitness distribution and show that the model exhibits a phase transition depending on the tail exponent of the fitness distribution. In the weak disorder regime, one of the old vertices has maximal degree irrespective of fitness, while for strong disorder the vertex with maximal degree has to satisfy the right balance between fitness and age. Our methods use martingale methods to show concentration of degree evolutions as well as extreme value theory to control the fitness landscape.


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Bas Lodewijks. Marcel Ortgiese. "A phase transition for preferential attachment models with additive fitness." Electron. J. Probab. 25 1 - 54, 2020.


Received: 20 March 2020; Accepted: 11 November 2020; Published: 2020
First available in Project Euclid: 18 December 2020

Digital Object Identifier: 10.1214/20-EJP550

Primary: 05C80
Secondary: 60G42


Vol.25 • 2020
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